An initial-boundary-value problem that approximate the quarter-plane problem for the Korteweg-de Vries equation

被引：31

作者：

Colin, T

Gisclon, M

机构：

[1] Univ Bordeaux 1, F-33405 Talence, France

[2] CNRS ESA 5466, F-33405 Talence, France

[3] Univ Savoie, Math Lab, F-73376 Le Bourget Du Lac, France

[4] CNRS EP 2067, F-73376 Le Bourget Du Lac, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2001年 / 46卷 / 06期

关键词：

Korteweg-de Vries; boundary conditions; smoothing effects; quarter plane;

D O I：

10.1016/S0362-546X(00)00155-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Korteg-de Vries equation was studied in order to describe the propogation of long water waves in a channel. An initial-boundary-value problem for the equation was studied and a local existence theorem was established. The smoothing effects were also considered and a finite difference scheme was applied to obtain the unconditional stability for the nonlinear version of the scheme.

引用

页码：869 / 892

页数：24

共 50 条

[1] AN INITIAL-BOUNDARY-VALUE PROBLEM FOR THE MODIFIED KORTEWEG-DE VRIES EQUATION IN A QUARTER PLANE
Shen Caixia
Guo Boling
[J]. JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2005, 18 (04): : 311 - 321
[2] The initial boundary problem for the Korteweg-de Vries equation on the negative quarter-plane
Marchant, TR
Smyth, NF
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2002, 458 (2020): : 857 - 871
[3] An initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
Leach, J. A.
Shaw, S.
[J]. WAVE MOTION, 2010, 47 (02) : 85 - 102
[4] NONLINEAR QUARTER-PLANE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION
Larkin, Nikolai A.
Tronco, Eduardo
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2011,
[5] The Initial-Boundary Value Poblem for the Korteweg-de Vries Equation on the Positive Quarter-Plane
Pham Loi Vu
[J]. Journal of Nonlinear Mathematical Physics, 2007, 14 : 28 - 43
[6] The initial-boundary value poblem for the Korteweg-de Vries equation on the positive quarter-plane
Vu, Pham Loi
[J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2007, 14 (01) : 28 - 43
[7] A mixed initial-boundary-value problem for the Korteweg-de Vries equation on a bounded interval
Colin, T
Ghidaglia, JM
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (05): : 599 - 603
[8] The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
Leach, J. A.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (04) : 1206 - 1228
[9] The initial-boundary value problem for the Korteweg-de Vries equation
Holmer, Justin
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (08) : 1151 - 1190
[10] A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
Bona, JL
Sun, SM
Zhang, BY
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (02) : 427 - 490

← 1 2 3 4 5 →